Problem: Which of the following ordered pairs represents a solution to the equation below? $(-2, -7) (-1, -5) (0, -2) (1, 3) (2, 7)$ $y = 3x-1$
Solution: We can try plugging in the x-value of each ordered pair into the equation. If we evaluate and get the y-value of the ordered pair, then that ordered pair is a solution! Let's consider $(-2, -7)$ If we plug in $-2$ for $x$ and evaluate, do we get $-7$ $y = (3)(-2) - 1 = -6 - 1 = -7$ Let's consider $(-1, -5)$ If we plug in $-1$ for $x$ and evaluate, do we get $-5$ $y = (3)(-1) - 1 = -3 - 1 = -4$ Let's consider $(0, -2)$ If we plug in $0$ for $x$ and evaluate, do we get $-2$ $y = (3)(0) - 1 = 0 - 1 = -1$ Let's consider $(1, 3)$ If we plug in $1$ for $x$ and evaluate, do we get $3$ $y = (3)(1) - 1 = 3 - 1 = 2$ Let's consider $(2, 7)$ If we plug in $2$ for $x$ and evaluate, do we get $7$ $y = (3)(2) - 1 = 6 - 1 = 5$ Thus the only ordered pair that is a solution to the equation is $(-2, -7)$ We come to the same answer by plotting the points and the equation. $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$ $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$